How do I extract 2D pictures from a 360 HDRI?
Add this equirectangular texture as world background texture as usual and render it.
By another words - go to Shader editor &gt; World tab, add Environment texture node
(not an Image texture node) and choose directory to HDR image on your drive.

Tips:

since you need only get render of BG, a Camera location doesn't matter
(would be different story if you would like to reconstruct envi)
to easy set view direction (camera rotation) it's handy go to 3D view editor &gt; Properties (N) side panel &gt; View tab &gt; View &gt; View Lock &gt; and enable Camera to View
Wrapping amount (distortion) of rendered image is equal to camera lens value. Range of view you can change in Properties editor &gt; Camera &gt; Lens &gt; Focal Length
use the highest hdri resolution available, since final render use just a portion of the texture, it is possible it would not be enough for backplate in some cases anyway :)
since source texture is high dynamic range (HDR) image it's useful to keep Color Management &gt; Filmic with some Look preset or adjust contrast later